Review WS 7 2 maanden vertraagd

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Fri, 27 Nov 2009 04:45:11 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/27/t1259322431cfq5u9gsdlhq9jn.htm/, Retrieved Fri, 27 Nov 2009 12:47:24 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Nov/27/t1259322431cfq5u9gsdlhq9jn.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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0 6.5 6.3 6.1 0 6.6 6.5 6.3 0 6.5 6.6 6.5 0 6.2 6.5 6.6 0 6.2 6.2 6.5 0 5.9 6.2 6.2 0 6.1 5.9 6.2 0 6.1 6.1 5.9 0 6.1 6.1 6.1 0 6.1 6.1 6.1 0 6.1 6.1 6.1 0 6.4 6.1 6.1 0 6.7 6.4 6.1 0 6.9 6.7 6.4 0 7 6.9 6.7 0 7 7 6.9 0 6.8 7 7 0 6.4 6.8 7 0 5.9 6.4 6.8 0 5.5 5.9 6.4 0 5.5 5.5 5.9 0 5.6 5.5 5.5 0 5.8 5.6 5.5 0 5.9 5.8 5.6 0 6.1 5.9 5.8 0 6.1 6.1 5.9 0 6 6.1 6.1 0 6 6 6.1 0 5.9 6 6 0 5.5 5.9 6 0 5.6 5.5 5.9 0 5.4 5.6 5.5 0 5.2 5.4 5.6 0 5.2 5.2 5.4 0 5.2 5.2 5.2 0 5.5 5.2 5.2 1 5.8 5.5 5.2 1 5.8 5.8 5.5 1 5.5 5.8 5.8 1 5.3 5.5 5.8 1 5.1 5.3 5.5 1 5.2 5.1 5.3 1 5.8 5.2 5.1 1 5.8 5.8 5.2 1 5.5 5.8 5.8 1 5 5.5 5.8 1 4.9 5 5.5 1 5.3 4.9 5 1 6.1 5.3 4.9 1 6.5 6.1 5.3 1 6.8 6.5 6.1 1 6.6 6.8 6.5 1 6.4 6.6 6.8 1 6.4 6.4 6.6

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 1.26367368122718 + 0.00440114533689808x[t] + 1.40345082424960y1[t] -0.576928969828826y2[t] + 0.006338650422903M1[t] -0.207233201114077M2[t] -0.214352974333265M3[t] -0.243844989034858M4[t] -0.197231539999112M5[t] -0.279849567342826M6[t] + 0.0186804379108398M7[t] -0.414227973933947M8[t] -0.269348540276246M9[t] -0.278787619681992M10[t] -0.183889745448256M11[t] -0.00166891303737878t + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 1.26367368122718 0.460064 2.7467 0.00915 0.004575 x 0.00440114533689808 0.099783 0.0441 0.96505 0.482525 y1 1.40345082424960 0.138376 10.1423 0 0 y2 -0.576928969828826 0.145249 -3.972 0.000307 0.000153 M1 0.006338650422903 0.133777 0.0474 0.962457 0.481228 M2 -0.207233201114077 0.141044 -1.4693 0.149987 0.074994 M3 -0.214352974333265 0.141761 -1.5121 0.138788 0.069394 M4 -0.243844989034858 0.14406 -1.6927 0.098706 0.049353 M5 -0.197231539999112 0.143918 -1.3704 0.178591 0.089296 M6 -0.279849567342826 0.139771 -2.0022 0.052437 0.026219 M7 0.0186804379108398 0.14162 0.1319 0.895755 0.447878 M8 -0.414227973933947 0.135264 -3.0624 0.004021 0.002011 M9 -0.269348540276246 0.137015 -1.9658 0.056657 0.028328 M10 -0.278787619681992 0.13519 -2.0622 0.046076 0.023038 M11 -0.183889745448256 0.134215 -1.3701 0.178691 0.089346 t -0.00166891303737878 0.003155 -0.529 0.599913 0.299957 Multiple Linear Regression - Regression Statistics Multiple R 0.956170284263282 R-squared 0.914261612508126 Adjusted R-squared 0.880417512182387 F-TEST (value) 27.0139139084398 F-TEST (DF numerator) 15 F-TEST (DF denominator) 38 p-value 1.11022302462516e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.188181322950762 Sum Squared Residuals 1.34566399168495 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.5 6.59081689542933 -0.0908168954293293 2 6.6 6.54088050173912 0.0591194982608785 3 6.5 6.55705110394175 -0.0570511039417492 4 6.2 6.32785219679493 -0.127852196794934 5 6.2 6.0094543825013 0.190545617498696 6 5.9 6.09824613306886 -0.198246133068860 7 6.1 5.97407197801027 0.125928021989732 8 6.1 5.99326350892667 0.106736491073331 9 6.1 6.02108823558123 0.0789117644187742 10 6.1 6.0099802431381 0.0900197568618983 11 6.1 6.10320920433446 -0.00320920433445819 12 6.4 6.28543003674533 0.114569963254665 13 6.7 6.71113502140574 -0.0111350214057395 14 6.9 6.74385081315761 0.156149186842389 15 7 6.84267360080232 0.157326399197683 16 7 6.83647196152254 0.163528038477462 17 6.8 6.82372360053802 -0.0237236005380234 18 6.4 6.45874649530701 -0.0587464953070114 19 5.9 6.30961305178923 -0.409613051789225 20 5.5 5.40408190271379 0.0959180972862084 21 5.5 5.27437657854869 0.225623421451313 22 5.6 5.49404017403709 0.105959825962906 23 5.8 5.72761421765841 0.0723857823415904 24 5.9 6.13283231793632 -0.232832317936324 25 6.1 6.16246134378104 -0.0624613437810437 26 6.1 6.17021784707372 -0.0702178470737203 27 6 6.04604336685139 -0.0460433668513886 28 6 5.87453735668746 0.125462643312543 29 5.9 5.97717478966871 -0.0771747896687065 30 5.5 5.75254276686266 -0.252542766862656 31 5.6 5.54571642636199 0.0542835736380142 32 5.4 5.48225577183631 -0.0822557718363094 33 5.2 5.28708323062383 -0.0870832306238308 34 5.2 5.11067086729655 0.0893291327034486 35 5.2 5.31928562245867 -0.119285622458673 36 5.5 5.50150645486955 -0.00150645486955109 37 5.8 5.93161258486685 -0.131612584866852 38 5.8 5.96432837661872 -0.164328376618725 39 5.5 5.78246099941351 -0.28246099941351 40 5.3 5.33026482439966 -0.0302648243996594 41 5.1 5.26759788649675 -0.167597886496755 42 5.2 5.01800657523151 0.181993424768492 43 5.8 5.57059854383852 0.229401456161479 44 5.8 5.92039881652323 -0.12039881652323 45 5.5 5.71745195524626 -0.217451955246256 46 5 5.28530871552825 -0.285308715528253 47 4.9 4.84989095554846 0.0501090444515413 48 5.3 5.18023119044879 0.119768809551209 49 6.1 5.80397415451703 0.296025845482965 50 6.5 6.48072246141082 0.019277538589177 51 6.8 6.57177092899104 0.228229071008965 52 6.6 6.73087366059541 -0.130873660595411 53 6.4 6.32204934079521 0.0779506592047891 54 6.4 6.07245802952997 0.327541970470034 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.795783884580208 0.408432230839585 0.204216115419792 20 0.682348534736579 0.635302930526843 0.317651465263421 21 0.685941039915583 0.628117920168835 0.314058960084417 22 0.709704610357758 0.580590779284485 0.290295389642242 23 0.753595469592615 0.492809060814769 0.246404530407384 24 0.83089636400324 0.338207271993522 0.169103635996761 25 0.74542956007117 0.509140879857659 0.254570439928830 26 0.696898511792478 0.606202976415045 0.303101488207523 27 0.604022630547026 0.791954738905948 0.395977369452974 28 0.717394918821008 0.565210162357983 0.282605081178992 29 0.760123537324182 0.479752925351636 0.239876462675818 30 0.730642270146895 0.53871545970621 0.269357729853105 31 0.71714998259752 0.565700034804958 0.282850017402479 32 0.665587924323412 0.668824151353176 0.334412075676588 33 0.600538382165116 0.798923235669768 0.399461617834884 34 0.644755659817614 0.710488680364771 0.355244340182386 35 0.474473686778345 0.94894737355669 0.525526313221655 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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